ML Aggarwal Solution Class 10 Chapter 3 Shares and Dividends Test

Test

Question 1

If a man received ₹1080 as dividend from 9% ₹20 shares, find the number of shares purchased by him.

Sol :

Income on one share $=\frac{g}{10 n} \times 20$

$=\operatorname{Rs} \frac{9}{5}$

∴No. of shares $=1080 \times \frac{5}{9}$

= 120 x 5 = 600

Question 2

Find the percentage interest on capital invested in 18% shares when a Rs 10 share costs Rs 12.

Sol :

Dividend on one share = 18% of Rs 10

$=\frac{18 \times 10}{100}$

$=Rs \frac{9}{5}$

Income on $₹ 12=\frac{9}{5}$

Then income of $₹ 100=\frac{9}{5} \times \frac{100}{12}=15$

∴Percentage interest on capital=15 %

Question 3

Rohit Kulkami invests Rs 10000 in 10% Rs 100 shares of a company. If his annual dividend is Rs 800, find :

(i) The market value of each share.

(ii) The rate percent which he earns on his investment.

Sol :

Investment = Rs 10000

Face value of each share = Rs 100

Rate of dividend = 10%

Annual dividend = Rs 800

∴ Market value $=\frac{10000 \times 10}{800}=₹ 125$

(ii) Rate percent on investment

$=\frac{800 \times 100}{10000}=8 \%$

Question 4

At what price should a 9% Rs 100 share be quoted when the money is worth 6% ?

Sol :

If interest is 6 then investment = Rs 100

and if interest is 9, then investment

$=\operatorname{Rs} \frac{100 \times 9}{6}$

=Rs 150

Market value of each share = Rs 150

Question 5

By selling at Rs 92, some 2.5% Rs 100 shares and investing the proceeds in 5% Rs 100 shares at Rs 115, a person increased his annual income by Rs 90. Find:

(i) the number of shares sold.

(ii) the number of shares purchased.

(iii) the new income.

(iv) the rate percent which he earns on his investment.

Sol :

Rate of dividend = 2.5% and market price = Rs 92

Let number of shares purchased = x.

Selling price of x shares = 92 x

Income from investing

$₹ x=\frac{92 x \times 2 \cdot 5}{92}$

$=\frac{92 x \times 25}{92 \times 10}=\frac{5}{2} x$

Again by investing 92x in 5% at 115

The dividend $=\frac{92 x \times 5}{115}=4 x$

Difference $=4 x-\frac{5}{2} x=\frac{3}{2} x$

∴$\frac{3}{2} x=90$

⇒$x=\frac{90 \times 2}{3}=60$

(i) ∴No. of shares=60

(ii) No. of shares sold $=\frac{92 x}{115}$

$\frac{92 \times 60}{115}=48$

(iii) New income =4x=4×60=₹ 240

(iv) Rate percent interest on investment

$=\frac{5 \times 100}{115}=\frac{100}{23}$

$=4 \frac{8}{23} \%$

Question 6

A man has some shares of Rs. 100 par value paying 6% dividend. He sells half of these at a discount of 10% and invests the proceeds in 7% Rs. 50 shares at a premium of Rs. 10. This transaction decreases his income from dividends by Rs. 120. Calculate:

(i) the number of shares before the transaction.

(ii) the number of shares he sold.

(iii) his initial annual income from shares.

Sol :

Let no. of shares = x

Value of x shares = x × 100 = 100 x

and dividend$=\frac{100 x \times 6}{100}=\mathrm{Rs} .6 x$

and dividend on half-shares $=$ Rs. $\frac{6 x}{2}=$ Rs. $3 x$

Now, no. of shares he sold out $=\frac{x}{2}$

Amount received at $10 \%$ discount

$=\frac{x}{2} \times 90=$ Rs. $45 x$

In investing Rs 45x, no. shares he purchased$=\frac{45 x}{60}$

∴Amount of shares $=\frac{45 x}{60} \times 50=$ Rs. $\frac{225 x}{6}$

Income at the rate of $7 \%=\frac{225}{6} x \times \frac{7}{100}=\frac{21 x}{8}$

Difference in income$=3 x-\frac{21 x}{8}=\frac{3 x}{8}$

According to the condition, $\frac{3 x}{8}=120$

$x=\frac{120 \times 8}{3}=320$

(i) ∴No. of share he hold initially =320

(ii) No. of shares he hold later $=\frac{320}{2}=160$

(iii) Amount of income initially =320×6

=Rs 1920

Question 7

Divide Rs. 101520 into two parts such that if one part is invested in 8% Rs. 100 shares at 8% discount and the other in 9% Rs. 50 shares at 8% premium, the annual incomes are equal.

Sol :

Total investment = Rs. 101520

Let investment in first part = x

and in second part = (101520 – x)

Market value of first kind of shares = Rs. 100 – Rs. 8

= Rs. 92

and rate of dividend = 8%

∴Dividend $=\frac{x \times 8}{92}=\operatorname{Rs} . \frac{2 x}{23}$

Marked value of second kind=(101520-x)

Rate of dividend=9%

and Market value= Rs. $\frac{100+8}{100} \times 50=\frac{108}{100} \times 50$

=Rs 54

∴Dividend $=(101520-x) \times \frac{9}{2 \times 54}=\frac{101520-x}{12}$

∴According to the sum $\frac{2 x}{23}=\frac{101520-x}{12}$

⇒24x=101520×23-23x

⇒24x+23x=101520×23

⇒47x=101520×23

∴$x=\frac{101520 \times 23}{47}=49680$

∴Investment of first part=Rs 49680 and in second part

=Rs 1015620-Rs 49680=Rs 51840

Question 8

A man buys Rs. 40 shares of a company which pays 10% dividend. He buys the shares at such a price that his profit is 16% on his investment. At what price did he buy each share ?

Sol :

Face value of each share = Rs. 40

Dividend = 10%

Gain on investment = 10%

∴Dividend on Rs. $40=\frac{40 \times 10}{100}=\operatorname{Rs} .4$

Now Rs. 16 is interest on the market value=Rs 100

∴Market value if interest is Rs. 4

$=\frac{100 \times 4}{16}=$ Rs. 25